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Triangle read by rows: replace A003983(n,k) with F(n).
4

%I #5 Mar 03 2013 13:23:23

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,3,2,1,1,1,1,2,3,3,2,

%T 1,1,1,1,2,3,5,3,2,1,1,1,1,2,3,5,5,3,2,1,1,1,1,2,3,5,8,5,3,2,1,1,1,1,

%U 2,3,5,8,8,5,3,2,1,1

%N Triangle read by rows: replace A003983(n,k) with F(n).

%F Replace term A003983(n,k) with F(n).

%F Triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(F(j+1)-F(j))}. [From _Paul Barry_, Jan 18 2009]

%e First few rows of A003983 are [1; 1,1; 1,2,1; 1,2,2,1;...] which become [F(1); F(1),F(1); F(1),F(2),F(1); F(1),F(2),F(2),F(1);...] =

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 1, 1;

%e 1, 1, 2, 1, 1;

%e 1, 1, 2, 2, 1, 1;

%e 1, 1, 2, 3, 2, 1, 1;

%e 1, 1, 2, 3, 3, 2, 1, 1;

%e 1, 1, 2, 3, 5, 3, 2, 1, 1;

%e 1, 1, 2, 3, 5, 5, 3, 2, 1, 1;

%e 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1;

%e ...

%Y Cf. A134404.

%K nonn,tabl

%O 1,13

%A _Gary W. Adamson_ & Klaus Breyer, Apr 10 2008